An asymptotic behavior of QR decomposition

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Abstract

The m-th root of the diagonal of the upper triangular matrix Rm in the QR decomposition of AXmB = QmRm converges and the limit is given by the moduli of the eigenvalues of X with some ordering, where A, B, X ∈ Cn × n are nonsingular. The asymptotic behavior of the strictly upper triangular part of Rm is discussed. Some computational experiments are discussed. © 2006 Elsevier Inc. All rights reserved.

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Huang, H., & Tam, T. Y. (2007). An asymptotic behavior of QR decomposition. Linear Algebra and Its Applications, 424(1 SPEC. ISS.), 96–107. https://doi.org/10.1016/j.laa.2006.02.043

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